Image reconstruction method in NMR imaging

Abstract

An image reconstruction method in an NMR imaging such as an echo-planar method, a fast Fourier imaging method or a fast spectroscopic imagin method is disclosed in which a spin-echo train is measured by use of an oscillating field gradient to obtain an actual measurement data train having a k-trajectory having positive and negative gradients on a k-space. A desired nuclear spin distribution is produced by establishing a predetermined trial image, subjecting each data in the trial image to a phase shift corresponding to the gradient of the k-trajectory and thereafter subjecting the phase-shifted trial image to inverse Fourier transformation to produce virtual measurement data trains which coincide in coordinates with the actual measurement data train, determining a difference between each data in the virtual measurement data train and the corresponding data in the actual measurement data train and making the sum of the absolute values of all of the differences or the sum of squares of the absolute values of all of the differences, and successively modifying the trial image so that the sum becomes small.

We claim: 
     
       1. An image reconstruction method in a nuclear magnetic resonance imaging system comprising magnetic field generating means for generating a static magnetic field, field gradients and an RF magnetic field, signal detecting means for detecting a nuclear magnetic resonance signal from an object to be examined, a computer for performing an operation on a signal detected by said signal detecting means, and output means for outputting the results of operation by said computer, said method comprising: (i) a step of detecting the nuclear magnetic resonance signal after nuclear spins in a predetermined space including said object to be examined have been excited and in a state in which there exist a first field gradient along a first direction of said predetermined space which is temporarily steady and a second field gradient along a second direction of said predetermined space which has a sense periodically inverted, thereby obtaining an actual measurement data train having on a k-space a k-trajectory which has a gradient caused by said first and second field gradients;   (ii) a step of subjecting a predetermined trial image m(I, J) to a phase shift ξ(μ, J) corresponding to the gradient of said k-trajectory and thereafter to inverse Fourier transformation, thereby obtaining a first virtual measurement data train M P  (μ, ν);   (iii) a step of subjecting a version of said trial image m(I, J) having an inverted sign of I to said phase shift ξ(μ, J) and thereafter to inverse Fourier transformation, thereby obtaining a second virtual measurement data train M N  (μ, ν);   (iv) a step of determining a difference (M P  -F P ) between each of data in said actual measurement data train in periods when said second field gradient is positive and data in said first virtual measurement data train at a position on said k-space corresponding thereto and a difference (M N  -F N ) between each of data in said actual measurement data train in periods when said second field gradient is negative and data in said second virtual measurement data train at a position on said k-space corresponding thereto and making the sum of the absolute values of all of the differences or the sum of squares of the absolute values of all of the differences;   (v) a step of modifying said trial image m(I, J) so that said sum of the absolute values of the differences or said sum of squares of the absolute values of the differences becomes small; and   (vi) a step of repeating said steps (i) to (v) to obtain an estimated image representative of the distribution of nuclear spins in said predetermined space.   
     
     
       2. An image reconstruction method according to claim 1, wherein said second field gradient is a magnetic field oscillating in a rectangular waveform and said phase shift ξ(μ, J) is ##EQU24## where L x  is the size of a field of view in said first direction, Δy is the size of a pixel in said second direction and M is the number of pixels in said first direction. 
     
     
       3. An image reconstruction method according to claim 1, wherein said second field gradient is a magnetic field oscillating in a sinusoidal waveform represented by G x  cos ωt and said phase shift ξ(μ, J) is ##EQU25## where η=(γG y  /ω) arcsin [(ω/γG x )k x  ], γ being the gyromagnetic ratio, G y  being the amplitude of said first field gradient and k x  being the spatial angular frequency in said second direction. 
     
     
       4. An image reconstruction method according to claim 1, wherein the modification of said trial image m(I, J) is made in such a manner that each of said differences (M P  -F P ) and (M N  -F N ) is subjected to another phase shift -ξ(μ, J) having a sign reverse to said phase shift ξ(μ, J) and thereafter to Fourier transformation, the results of the respective Fourier transformations are added to determine A(I, J) and the respective m(I, J) are modified in the direction of a gradient calculated in a form including A(I, J). 
     
     
       5. An image reconstruction method in a nuclear magnetic resonance imaging system comprising magnetic field generating means for generating a static magnetic field, field gradients and an RF magnetic field, signal detecting means for detecting a nuclear magnetic resonance signal from an object to be examined, a computer for performing an operation on a signal detected by said signal detecting means, and output means for outputting the results of operation by said computer, said method comprising: (i) a step of detecting the nuclear magnetic resonance signal after nuclear spins in a predetermined space including said object to be examined have been excited and in a state in which a first field gradient along a first direction of said predetermined space is zero and a second field gradient along a second direction of said predetermined space having a sense periodically inverted exists, thereby obtaining an actual measurement data train having on a k-space a k-trajectory which has a gradient caused by a chemical shift of said nuclear spins and said second field gradient;   (ii) a step of subjecting a predetermined trial image m(I, J) in an orthogonal coordinate system to a phase shift ξ(η, J) corresponding to the gradient of said k-trajectory and thereafter to inverse Fourier transformation, thereby obtaining a first virtual measurement data train M P  (μ, ν);   (iii) a step of subjecting a version of said trial image m(I, J) having an inverted sign of I to said phase shift ξ(μ, J) and thereafter to inverse Fourier transformation, thereby obtaining a second virtual measurement data train M N  (μ, ν);   (iv) a step of determining a difference (M P  -F P ) between each of data in said actual measurement data train in periods when said second field gradient is positive and data in said first virtual measurement data train at a position on said k-space corresponding thereto and a difference (M N  -F N ) between each of data in said actual measurement data train in periods when said second field gradient is negative and data in said second virtual measurement data train at a position on said k-space corresponding thereto and making the sum of the absolute values of all of the differences or the sum of squares of the absolute values of all of the differences;   (v) a step of modifying said trial image m(I, J) so that said sum of the absolute values of the differences or said sum of squares of the absolute values of the differences becomes small; and   (vi) a step of repeating said steps (i) to (v) to obtain an estimated image representative of the distribution of nuclear spins in said predetermined space having an axis of said second direction and a chemical shift axis as coordinate axes.